Verified answer

おはよう = 'Morning

おはようございます = Good morning

Ohayou is the respectful form of the adjective hayai with this form you must use a verb that agrees with it. So you could not say ohayou aru or ohayou arimasu. or ohayou da or ohayou desu. because those words are not respectful enough. So you say ohayou gozaimasu.

Similiarly Arigatou is the respectful form of the adjective arigatai. It changes to arigatou and takes a respectful verb form as well arigatou gozaimasu.

Sometimes you may not even notice it. However the farewell greeting sayounara is using the respectful from of the word sou you know as in sou desu ne. If you wanted to say this in respectful language it would sayou de gozaimasu ne. (I threw in the ne as a kind of little joke)

As far as I know that is the only way to say good morning. Both are relatively respectful. the one with gozaimasu "maybe" a little more respectful.

おはよう is less polite than おはようございます

I'm not aware of any other ways that are literally "good morning" but I'm not fluent by any scale.